math question 1 week 7

Question

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many type of solutions?
Please provide the name for each type of solution.

Answer 1

Type of solution of quadratic depends on the value of Discriminant:  b^2 - 4ac

 

  Roots are evaluated by factoring the equation of 

 

   aX^2 + bx + c

 

  a ( X - b/ 2a ) ^2 - ( b^2 - 4ac)/ 4a^2  

 

   X₁ , X₂  = -b/2a ±√(b^2 - 4ac) /2a

 

     if   b^2 - 4ac > 0  , then quadratic has 2 real roos

       

               a.  b^2 -4ac is a perfect square then the roots are rational

 

               b . b^2 - 4ac not a perfect square, then the roots are irrational

    if  b^2 - 4ac< 0 , then quadratic has 2 complex roots.

 

      Quadratic always has 2 roots.

         The irrational and complex roots has to appear as conjugate pair for the coefficients of the quadratic

          to be integers.

 

        i.e. 

 

                X = a ± bi 

                

                 X = a ± √b